Binary Additive Problems: Theorems of Landau and Hardy-littlewood Type

The Hardy-landau-littlewood Inequalities with Less Smoothness

One proves Hardy-Landau-Littlewood type inequalities for functions in the Lipschitz space attached to a C0-semigroup (or to a C 0 -semigroup).

Note on the Converses of Inequalities of Hardy and Littlewood

The inequalities of Hardy–Littlewood type play very important role in many theorems concerning convergence or summability of orthogonal series. In the applications many times their converses are also very useful. Both the original inequalities and their converses have been generalized in several directions by many authors, among others Leindler (see [5], [6], [7], [8]), Mulholland (see [10]), C...

Hardy-Littlewood Theorems for A-Harmonic Tensors

Additive Problems with Prime Variables the Circle Method of Hardy, Ramanujan and Littlewood

In these lectures we give an overview of the circle method introduced by Hardy and Ramanujan at the beginning of the twentieth century, and developed by Hardy, Littlewood and Vinogradov, among others. We also try and explain the main difficulties in proving Goldbach’s conjecture and we give a sketch of the proof of Vinogradov’s three-prime Theorem. 1. ADDITIVE PROBLEMS In the last few centuries...

Inequalities of Hardy-Littlewood-Polya Type for Functions of Operators and Their Applications

In this paper, we derive a generalized multiplicative Hardy-LittlewoodPolya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of a function of an operator on a class of elements defined with the help of another function of the operator. We then apply the results to solve the following p...